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双曲空間における測地線のスペクトル的性質の解明

阐明双曲空间测地线的光谱特性

基本信息

批准号：
07J10925
负责人：
桐山麻貴 (中筋麻貴)
金额：
$ 1.34万
依托单位：
Tsuda College
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2007
资助国家：
日本
起止时间：
2007 至 2009
项目状态：
已结题

项目摘要

連続スペクトルの分布状況の解明には,保型L関数の解析が必要となる.その初期段階として,関連するspherical representationの性質を解明することを目的とした.p-進群Gの球面表示において,Casselman(1980)が標準絡作用素に双対となるベクトル基底(Casselman基底)を定義した.本年度はこの基底を明示的に記述することを試みた.米国Stanford大学のBump教授との共同研究において,G=GL(3)において具体的記述を得ることに成功し,得られた成果を報告集(津田塾大学数学・計算機科学研究所報告集)にまとめた.一方,ここで得られた各基底の表示には,一定の規則があるように見受けられた.これをもとにG=GL(4)について計算機を用いて調べた結果,ある一定条件のもとでその規則が成り立つことが判明した.この事から一般のGに関する予想をたて,これを6月の研究集会(Forth Workshop in Multiple Dirichlet series)で発表した.その後も本予想について研究を続け,A型ルート系においてBruhat順序で関連するワイル群の元に対し,"good word"の存在を仮定した所,この予想を解く事に成功した.本結果は論文にまとめ投稿中である.本研究の成果は組み合わせ論で知られるDeodhar予想や,未解決問題として知られるKazhdan-Lusztig多項式の情報を含む事から,スペクトルの分布状況のみならず,表現論,組み合わせ論において重要な成果となった.

In connection with the distribution of the information, the distribution of the system is explained, and the type-preserving L data is analyzed as necessary. In the early stage of the experiment, the spherical representation was used to understand the purpose of the test. P-the group G sphere represents the target, and the standard Casselman (1980) defines the substrate (Casselman base) of the standard hormone. This year, the base of this year is clearly stated in this year's account. Professor Bump of the University of Stanford in the United States co-studied the achievements of the Institute of Mathematical computer Science of Tsuda University. G=GL (3) received a detailed account of the success of the study. On the other hand, if you want to make sure that all the bases are affected, there must be some rules to ensure that they are affected. This is to verify the results of the G=GL (4) computer calculation machine, and to determine the accuracy of the rules under certain conditions. I don't know what to do. I don't want to. I don't want to. I don't want to talk about it. I don't know what to do. I don't want to talk about it. I don't know. I don't want to talk about it. I don't want to talk about it. I don't know what to do. I don't want to talk about it. In the future, I would like to know that I want to study the situation. Type An is the order of the Bruhat sequence. I want to know that there is a lot of data in the group, and that there is a place where I want to know how to solve the problem. The results of this paper show that there are some problems in the contribution. In this study, the results of this study show that the results of this study show that you are not aware of the Deodhar, and that you have not solved the problem. You know that the multi-item information system of Kazhdan-Lusztig contains information, information